Discussion of “Independent component analysis by robust distance correlation”: a note on the geometry of the bowl transform and on the reach of the consistency for robust ICA

This is a discussion of PICARD, the robust independent component analysis (ICA) estimator built on a transformed distance correlation and on the bowl transform. I develop two threads. The first reads the bowl transform as a multivariate redescending $$\psi$$ -function, makes its exponential decay explicit, and describes how the transformed norm concentrates as the dimension grows. The second examines the reach of the strong-consistency result, relating its population target to classical ICA identifiability and to the behavior of robust whitening under non-elliptical sources.